Recently, I study tiling of the plane with regular polygon which is edge-to edge.
If we restrict to the two triangles and two hexagons, then we can slide rows of tiles so that in adjacent rows, we either match triangle edges to triangle edges or we match triangle edges to hexagon edges, this implies that there exist infinity of distinct tilings by two triangles and two hexagons.
I would like to know the number of distinct tiling if type of every vertex is $3.6.3.6$?
Is it true that there is only one tiling such that type of every vertex is $3.6.3.6$?